/*
 * Unique Binary Search Trees
Given n, how many structurally unique BST's (binary search trees) that store values 1...n?

For example,
Given n = 3, there are a total of 5 unique BST's.

   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3
 */
package com.xinpan.exercise;

public class UniqueBST {
    public int numTrees(int n) {
        // Start typing your Java solution below
        // DO NOT write main() function
        if(n == 0 || n == 1)
            return 1;
            
        int sum = 0;
        for(int i = 0; i < n; i++)
        {
            int n1 = numTrees(i);
            int n2 = numTrees(n-i-1);
            sum += n1 * n2;
        }
        return sum;
    }
}
